cl2faces.vert.reg.tetra: The closest points among a data set in the vertex regions to...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The closest points among a data set in the vertex regions to the respective faces in a tetrahedron

Description

An object of class "Extrema". Returns the closest data points among the data set, Xp, to face i in M-vertex region i for i=1,2,3,4 in the tetrahedron th=T(A,B,C,D). Vertex labels are A=1, B=2, C=3, and D=4 and corresponding face labels are BCD=1, ACD=2, ABD=3, and ABC=4.

Vertex regions are based on center M which can be the center of mass ("CM") or circumcenter ("CC") of th.

Usage

cl2faces.vert.reg.tetra(Xp, th, M = "CM")

Arguments

Xp	A set of 3D points representing the set of data points.
th	A 4 \times 3 matrix with each row representing a vertex of the tetrahedron.
M	The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

Value

A list with the elements

txt1	Vertex labels are A=1, B=2, C=3, and D=4 (correspond to row number in Extremum Points).
txt2	A short description of the distances as "Distances from Closest Points to Faces ...".
type	Type of the extrema points
desc	A short description of the extrema points
mtitle	The "main" title for the plot of the extrema
ext	The extrema points, here, closest points to faces in the respective vertex region.
ind.ext	The data indices of extrema points, ext.
X	The input data, Xp, can be a matrix or data frame
num.points	The number of data points, i.e., size of Xp
supp	Support of the data points, here, it is th
cent	The center point used for construction of vertex regions, it is circumcenter of center of mass for this function
ncent	Name of the center, it is circumcenter "CC" or center of mass "CM" for this function.
regions	Vertex regions inside the tetrahedron th provided as a list.
region.names	Names of the vertex regions as "vr=1","vr=2","vr=3","vr=4"
region.centers	Centers of mass of the vertex regions inside th.
dist2ref	Distances from closest points in each vertex region to the corresponding face.

Author(s)

Elvan Ceyhan

See Also

fr2vertsCCvert.reg, fr2edgesCMedge.reg.std.tri, fr2vertsCCvert.reg.basic.tri and kfr2vertsCCvert.reg

Examples

## Not run: 
A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0);
D<-c(1/2,sqrt(3)/6,sqrt(6)/3)
set.seed(1)
tetra<-rbind(A,B,C,D)+matrix(runif(12,-.25,.25),ncol=3)
n<-10  #try also n<-20
Cent<-"CC"  #try also "CM"

n<-20  #try also n<-100
Xp<-runif.tetra(n,tetra)$g  #try also Xp<-cbind(runif(n),runif(n),runif(n))

Ext<-cl2faces.vert.reg.tetra(Xp,tetra,Cent)
Ext
summary(Ext)
plot(Ext)

clf<-Ext$ext

if (Cent=="CC") {M<-circumcenter.tetra(tetra)}
if (Cent=="CM") {M<-apply(tetra,2,mean)}

Xlim<-range(tetra[,1],Xp[,1],M[1])
Ylim<-range(tetra[,2],Xp[,2],M[2])
Zlim<-range(tetra[,3],Xp[,3],M[3])
xd<-Xlim[2]-Xlim[1]
yd<-Ylim[2]-Ylim[1]
zd<-Zlim[2]-Zlim[1]

plot3D::scatter3D(Xp[,1],Xp[,2],Xp[,3], phi =0,theta=40, bty = "g",
main="Closest Pointsin CC-Vertex Regions \n to the Opposite Faces",
xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05), zlim=Zlim+zd*c(-.05,.05),
          pch = 20, cex = 1, ticktype = "detailed")
#add the vertices of the tetrahedron
plot3D::points3D(tetra[,1],tetra[,2],tetra[,3], add=TRUE)
L<-rbind(A,A,A,B,B,C); R<-rbind(B,C,D,C,D,D)
plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lwd=2)
plot3D::points3D(clf[,1],clf[,2],clf[,3], pch=4,col="red", add=TRUE)

plot3D::text3D(tetra[,1],tetra[,2],tetra[,3],
labels=c("A","B","C","D"), add=TRUE)

#for center of mass use #Cent<-apply(tetra,2,mean)
D1<-(A+B)/2; D2<-(A+C)/2; D3<-(A+D)/2;
D4<-(B+C)/2; D5<-(B+D)/2; D6<-(C+D)/2;
L<-rbind(D1,D2,D3,D4,D5,D6); R<-rbind(M,M,M,M,M,M)
plot3D::segments3D(L[,1], L[,2], L[,3], R[,1], R[,2],R[,3], add=TRUE,lty=2)

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.